Specifically, this is about the bulldozer attack yesterday. Honest Reporting's Backspin blog (Hat tip: Cosmic X) features some screenshot examples of how the Beeb lied about the bus, for example: they said it was an empty bus, when as it so happens, there were schoolgirls in it. In the third picture, they omitted the bus part altogether.
And there's little chance that we can ever expect them to improve. I won't be surprised if tons of people in Britain foolishly rely more on the MSM than they do in the US, and that's why they're able to get away with much of it.